Description Details Distributions Functionals for Distributions Models and Estimators Diagnostics Starting Point Classes Functions Generating Functions Methods Constants Acknowledgement Start-up-Banner Package versions Author(s) References See Also

RobExtremes provides infrastructure for speeded-up optimally robust estimation (i.e., MBRE, OMSE, RMXE) for extreme value distributions, extending packages distr, distrEx, distrMod, robustbase, RobAStBase, and ROptEst.

Package: | RobExtremes |

Version: | 1.1.0 |

Date: | 2018-08-03 |

Title: | Optimally Robust Estimation for Extreme Value Distributions |

Description: | Optimally robust estimation for extreme value distributions using S4 classes and methods |

(based on packages distr, distrEx, distrMod, RobAStBase, and ROptEst). | |

Depends: | R (>= 2.14.0), methods, distrMod(>= 2.5.2), ROptEst(>= 1.0), robustbase(>= 0.8-0), evd |

Suggests: | RUnit (>= 0.4.26), ismev (>= 1.39) |

Imports: | actuar, RobAStRDA, distr, distrEx, RandVar, RobAStBase, startupmsg |

Authors: | Bernhard Spangl [contributed smoothed grid values of the Lagrange multipliers] |

Sascha Desmettre [contributed smoothed grid values of the Lagrange multipliers] | |

Eugen Massini [contributed an interactive smoothing routine for smoothing the | |

Lagrange multipliers and smoothed grid values of the Lagrange multipliers] | |

Daria Pupashenko [contributed MDE-estimation for GEV distribution in the framework of | |

her PhD thesis 2011--14] | |

Gerald Kroisandt [contributed testing routines] | |

Nataliya Horbenko ["aut","cph"] | |

Matthias Kohl ["aut", "cph"] | |

Peter Ruckdeschel ["cre", "aut", "cph"], | |

Contact: | [email protected] |

ByteCompile: | yes |

LazyLoad: | yes |

License: | LGPL-3 |

URL: | http://robast.r-forge.r-project.org/ |

Encoding: | latin1 |

VCS/SVNRevision: | 1091 |

Importing from packages actuar, evd, it provides S4 classes and methods for the

Gumbel distribution

Generalized Extreme Value distribution (GEVD)

Generalized Pareto distribution (GPD)

Pareto distribution

These distributions come together with particular methods for expectations. I.e., a functional E() as in package distrEx, which as first argument takes the distribution, and, optionally, can take as second argument a function which then is used as integrand. These particular methods are available for the GPD, Pareto, Gamma, Weibull, and GEV disdribution and use integration on the quantile scale, i.e.,

*E[X] = integral_0^1 q^X(s) ds*

where *q^X* is the quantile function of X.
In addition, where they exist, we provide closed from expressions for
variances, median, IQR, skewness, kurtosis.

In addition, extending estimators `Sn`

and `Qn`

from package
robustbase, we provide functionals for Sn and Qn. A new
asymmetric version of the `mad`

, `kMAD`

gives yet another robust
scale estimator (and functional).

As to models, we provide the

GPD model (with known threshold), together with (speeded-up) optimally robust estimators, with LDEstimators (in general, and with

`medkMAD`

,`medSn`

and`medQn`

as particular ones) and Pickands' estimator as starting estimators.GEVD model (with known or unknown threshold), together with (speeded-up) optimally robust estimators, with LDEstimators (see above) and Pickands' estimator as starting estimators.

Pareto model

Weibull model

Gamma model

and for each of these, we provide speeded-up optimally robust estimation
(i.e., MBRE, OMSE, RMXE).

We robust (high-breakdown) starting estimators for

GPD (PickandsEstimator, medkMAD, medSn, medQn)

GEV (PickandsEstimator)

Pareto (Cram<e9>r-von-Mises-Minimum-Distance-Estimator)

Weibull (the quantile based estimator of Boudt/Caliskan/Croux)

Gamma (Cram<e9>r-von-Mises-Minimum-Distance-Estimator)

For all these families, of course, MLEs and Minimum-Distance-Estimators are also available through package "distrMod".

We bridge to the diagnostics provided by package "ismev", i.e. our
return objects can be plugged into the diagnostics of this package.

We have the usual diagnostic plots from package "RobAStBase", i.e.

Outylingness plots

`outlyingPlotIC`

IC plots

`plot`

Information plots via

`infoPlot`

IC comparison plots via

`comparePlot`

Cniperpoint plots (from package "ROptEst") via

`CniperPointPlot`

but also (adopted from package "distrMod")

qqplots (with confidence bands) via

`qqplot`

returnlevel plots via

`returnlevelplot`

As a starting point you may look at the included script
‘"RobFitsAtRealData.R"’ in the scripts folder of the package,
accessible by
```
file.path(system.file(package="RobExtremes"),
"scripts/RobFitsAtRealData.R")
```

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | ```
[*]: there is a generating function with the same name in RobExtremes
[**]: generating function from distrMod, but with (speeded-up)
opt.rob-estimators in RobExtremes
##########################
Distribution Classes
##########################
"Distribution" (from distr)
|>"UnivariateDistribution" (from distr)
|>|>"AbscontDistribution" (from distr)
|>|>|>"Gumbel" [*]
|>|>|>"Pareto" [*]
|>|>|>"GPareto" [*]
|>|>|>"GEVD" [*]
##########################
Parameter Classes
##########################
"OptionalParameter" (from distr)
|>"Parameter" (from distr)
|>|>"GumbelParameter"
|>|>"ParetoParameter"
|>|>"GEVDParameter"
|>|>"GParetoParameter"
##########################
ProbFamily classes
##########################
slots: [<name>(<class>)]
"ProbFamily" (from distrMod)
|>"ParamFamily" (from distrMod)
|>|>"L2ParamFamily" (from distrMod)
|>|>|>"L2GroupParamFamily" (from distrMod)
|>|>|>|>"ParetoFamily" [*]
|>|>|>|>"L2ScaleShapeUnion" (from distrMod)
|>|>|>|>|>"GammaFamily" [**]
|>|>|>|>|>"GParetoFamily" [*]
|>|>|>|>|>"GEVFamily" [*]
|>|>|>|>|>"WeibullFamily" [**]
|>|>|>|>"L2LocationScaleUnion" /VIRTUAL/ (from distrMod)
|>|>|>|>|>"L2LocationFamily" (from distrMod)
|>|>|>|>|>|>"GumbelLocationFamily" [*]
|>|>|>|>"L2LocScaleShapeUnion" /VIRTUAL/ (from distrMod)
|>|>|>|>|>"GEVFamilyMuUnknown" [*]
``` |

1 2 3 4 5 6 7 8 9 10 | ```
LDEstimator Estimators for scale-shape models based on
location and dispersion
medSn loc=median disp=Sn
medQn loc=median disp=Qn
medkMAD loc=median disp=kMAD
asvarMedkMAD [asy. variance to MedkMADE]
PickandsEstimator PickandsEstimator
asvarPickands [asy. variance to PickandsE]
QuantileBCCEstimator Quantile based estimator for the Weibull distribution
asvarQBCC [asy. variance to QuantileBCCE]
``` |

1 2 3 4 5 6 7 8 9 10 11 | ```
Distribution Classes
Gumbel Generating function for Gumbel-class
GEVD Generating function for GEVD-class
GPareto Generating function for GPareto-class
Pareto Generating function for Pareto-class
L2Param Families
ParetoFamily Generating function for ParetoFamily-class
GParetoFamily Generating function for GParetoFamily-class
GEVFamily Generating function for GEVFamily-class
WeibullFamily Generating function for WeibullFamily-class
``` |

1 2 3 4 5 6 7 8 9 10 11 | ```
Functionals:
E Generic function for the computation of
(conditional) expectations
var Generic functions for the computation of functionals
IQR Generic functions for the computation of functionals
median Generic functions for the computation of functionals
skewness Generic functions for the computation of functionals
kurtosis Generic functions for the computation of functionals
Sn Generic function for the computation of (conditional)
expectations
Qn Generic functions for the computation of functionals
``` |

1 2 |

This package is joint work by Peter Ruckdeschel, Matthias Kohl, and Nataliya Horbenko (whose PhD thesis went into this package to a large extent), with contributions by Dasha Pupashenko, Misha Pupashenko, Gerald Kroisandt, Eugen Massini, Sascha Desmettre, and Bernhard Spangl, in the framework of project "Robust Risk Estimation" (2011-2016) funded by Volkswagen foundation (and gratefully ackknowledged). Thanks also goes to the maintainers of CRAN, in particully to Uwe Ligges who greatly helped us with finding an appropriate way to store the database of interpolating functions which allow the speed up – this is now package RobAStRDA on CRAN.

You may suppress the start-up banner/message completely by setting
`options("StartupBanner"="off")`

somewhere before loading this package by
`library`

or `require`

in your R-code / R-session.
If option `"StartupBanner"`

is not defined (default) or setting
`options("StartupBanner"=NULL)`

or
`options("StartupBanner"="complete")`

the complete start-up banner is
displayed.
For any other value of option `"StartupBanner"`

(i.e., not in
`c(NULL,"off","complete")`

) only the version information is displayed.
The same can be achieved by wrapping the `library`

or `require`

call
into either `suppressStartupMessages()`

or
`onlytypeStartupMessages(.,atypes="version")`

.
As for general `packageStartupMessage`

's, you may also suppress all
the start-up banner by wrapping the `library`

or `require`

call into `suppressPackageStartupMessages()`

from
startupmsg-version 0.5 on.

Note: The first two numbers of package versions do not necessarily reflect package-individual development, but rather are chosen for the RobAStXXX family as a whole in order to ease updating "depends" information.

Peter Ruckdeschel [email protected],

Matthias Kohl [email protected], and

Nataliya Horbenko [email protected],

*Maintainer:* Peter Ruckdeschel [email protected]

M. Kohl (2005): *Numerical Contributions to the Asymptotic
Theory of Robustness.* PhD Thesis. Bayreuth. Available as
http://r-kurs.de/RRlong.pdf

P. Ruckdeschel, M. Kohl, T. Stabla, F. Camphausen (2006):
S4 Classes for Distributions, *R News*, *6*(2), 2-6.
https://CRAN.R-project.org/doc/Rnews/Rnews_2006-2.pdf

M. Kohl, P. Ruckdeschel, H. Rieder (2010):
Infinitesimally Robust Estimation in General Smoothly Parametrized Models.
*Stat. Methods Appl.*, **19**, 333–354.

Ruckdeschel, P. and Horbenko, N. (2011): Optimally-Robust Estimators in Generalized
Pareto Models. *Statistics*. **47**(4), 762–791.

Ruckdeschel, P. and Horbenko, N. (2012): Yet another breakdown point notion:
EFSBP –illustrated at scale-shape models. *Metrika*, **75**(8),
1025–1047.

A vignette for packages distr, distrSim, distrTEst,
and RobExtremes is included into the mere documentation package distrDoc
and may be called by `require("distrDoc");vignette("distr")`

.

A homepage to this package is available under http://robast.r-forge.r-project.org/.

`distr-package`

,
`distrEx-package`

,
`distrMod-package`

,
`RobAStBase-package`

,
`ROptEst-package`

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